## anonymous 5 years ago square root of 27 a^2b^3c^5

1. anonymous

$\sqrt{27a ^{2}b ^{3}c ^{5}}$

2. anonymous

3abc^2sqrt(3bc)

3. anonymous

27 = 3 times 3 times 3 = 3^2 times 3 b^3 = b^2 times b c^5 = c^2 times c^2 times c

4. anonymous

I know the answer I need an explanation

5. anonymous

so if you do sqrt (27) that is sqrt(3^3 times3) = 3sqrt3 similarly the others too follow the same pattern

6. anonymous

i meant sqrt(3^2 times3)

7. anonymous

ok im clear there what about the variables

8. anonymous

same thing. sqrt (a^2) = a sqrt(b^3) = b sqrt(b) sqrt(c^5) = c^2 sqrt(c)

9. anonymous

what is confusing me is the c^5 i see that c^2c^2 c = c^5

10. anonymous

yes c^2*c^2 = (c^2)^2

11. anonymous

so c^5 = (c^2)^2 times c

12. anonymous

ohhhhhhhhhhhhh your the best thanks so much

13. anonymous

you are welcome.

14. anonymous

for example, 16 = 4^2 but 4 = 2^2 so 4^2 = (2^2)^2 so sqrt 16 = sqrt(4^2) = sqrt (2^2)^2 = 2^2 = 4.